基于稀疏梯度场的非局部图像去噪算法

张瑞; 冯象初; 王斯琪; 常莉红

doi:10.16383/j.aas.2015.c140903

基于稀疏梯度场的非局部图像去噪算法

doi: 10.16383/j.aas.2015.c140903

1.
西安电子科技大学数学与统计学院西安 710126

基金项目:

国家自然科学基金(61271294,61105011,11101292,61379030,61362029,61101208),陕西省自然科学基金(2013JM1001)资助

详细信息

作者简介:
冯象初西安电子科技大学数学与统计学院教授.1999年获得西安电子科技大学理学博士学位.主要研究方向为数值分析,小波,图像处理的偏微分方程方法.E-mail:xcfeng@mail.xidian.edu.cn

王斯琪西安电子科技大学数学与统计学院博士研究生.主要研究方向为图像处理中的数学问题.E-mail:pearlwangxd@163.com

常莉红西安电子科技大学数学与统计学院博士研究生.主要研究方向为图像处理中的数学问题.E-mail:changlihong-1999@126.com

通讯作者:
张瑞西安电子科技大学数学与统计学院博士研究生.主要研究方向为稀疏表示和变分方法在图像处理中的应用.本文通信作者.E-mail:guanyue_002@163.com

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出版历程
- 收稿日期: 2014-12-30
- 修回日期: 2015-04-30
- 刊出日期: 2015-09-20

A Sparse Gradients Field Based Image Denoising Algorithm via Non-local Means

1.
School of Mathematics and Statistics, Xidian University, Xi'an 710126

Funds:

Supported by National Natural Science Foundation of China (61271294, 61105011, 11101292, 61379030, 61362029, 61101208) and Science Foundation of Shaanxi Province (2013JM1001)

摘要

摘要: 非局部平均(Non-local means, NLM)算法充分利用图像的自相似性与结构信息的冗余性, 取得了很好的去噪效果.然而, 在强噪声的干扰下, NLM算法中的权函数不能准确度量图像块之间的相似性. 因此, 很多文献利用图像的梯度信息对权函数做了改进.但是, 传统的梯度算子对噪声十分敏感, 不能有效地提高相似性度量的准确性. 本文将图像的稀疏梯度场(Sparse gradients field, SGF)引入权函数的定义中, 提出一种基于稀疏梯度场的非局部图像去噪算法. 首先, 区别于传统基于局部的梯度算子, 提出了基于全局的稀疏梯度场模型, 进一步给出一个自适应的稀疏梯度场模型(Adaptive sparse gradients field, ASGF), 并利用向前--向后分裂算法求解.然后, 利用图像的稀疏梯度场对NLM算法的权函数进行改进, 得到本文提出的算法.实验结果表明, 无论是客观评价还是视觉效果, 本文所提算法的性能优于NLM 算法和其他利用梯度信息改进的NLM算法.
- 图像去噪 /
- 非局部平均 /
- 稀疏梯度场 /
- 向前--向后分裂算法
Abstract: Non-local means (NLM) algorithm can obtain very good denoising results by making full use of the self-similarity and structural information's redundancy of images. But the weight function of NLM algorithm cannot accurately measure the similarity between image patches in the case of strong noise. Therefore, the weight function of NLM has been improved by using the gradients information of images in many papers. However, the traditional gradients operators cannot improve the accuracy of similarity measurement efficiently because they are sensitive to noise. This paper proposes a sparse gradients field (SGF) based image denoising algorithm via non-local means, in which the SGF of image is introduced to redefine the similarity measurement. First, a global sparse gradients field model and an adaptive sparse gradients field model are proposed which is different from traditional gradients operators and solved by forward-backward splitting algorithm. Then, the algorithm is proposed by redefining weight function via SGF. Experimental results demonstrate that compared with the NLM algorithm and other improved algorithms using information of gradients our proposed method has a better performance both in objective measurement and visual evaluation.
- Image denoising /
- non-local means (NLM) /
- sparse gradients field (SGF) /
- forward-backward splitting algorithm

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参考文献(17)

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